递归公式

Also asymptotic behavior of intermediate point of the error is studied and proved and, and the result is extended to Taylor's formula o...

然后研究了这种误差中的"中间点"的渐近性，给出了"中间点渐近性"的递归性的证明。本文并将讨论的结果推广到了多元Taylor公式。

The contents involve the recursion algorithms, the dual functional of SBGB basis and the transformation formula between SBGB basis and Bernstein basis.

给出它们的递归算法，SBGB基函数的对偶泛函，并由此得到SBGB基函数与Bernstein基函数转换公式。

And a new method of three kinds of recurrence sequences for general term formula was obtained.

获得了求三类递归数列通项公式的一种新方法。

In this paper a second order step size iteration formula is derived in detail and the recursive expression for the expanded N-order step size iteration formula is deduced.

文中详细推导了2阶步长迭代公式，并导出了扩展的N阶步长迭代公式的递归表达式。

Based on the Gaussian kernel function, the recursion formula of bandwidth is derived.

在未知总体分布的情形下，给出密度核估计中选择窗宽的一个新方法，并在选取高斯核的情形下，推导出计算窗宽的递归公式。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Furthermore, the equation of surface reflection seismogram generated by spherical wave pro.

利用弹性动力学方程变换和递归算法，计算了反射矩阵，从理论上推导了球面波在层状弹性半空间传播时产生的地面反射记录的计算公式。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次，分析了一般钟控停走组合生成器输出序列的概率分布性质，证明了生成器的输出序列是严平稳的，且服从强大数定律和中心极限定理；考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率，给出了符合率的具体计算公式；给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法，进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

We give a new 2-D graphical representation of protein sequences based on nucleotide triplet codons in the half complex plane, which has no degeneracy. Meanwhile using main characterization of complex vector: module and phase, we give a kind of numerical description of protein sequences.

利用这三个递归公式给出了RNA二级结构序列的1-D、2-D和3-D图形表示，进一步利用1-D图形表示给出了关于RNA二级结构序列频谱分析的方法。

Aiming at credit risk of loan portfolios in banks, this paper proposes a surplus process of a loan portfolio, and establishes a ruin model with finite and discrete time. Using this model, we derive the ruin probabilities and their recursive equations for the class with single loan amount and the class with multiple loan amounts.

摘 要：本文针对银行贷款组合中的信用风险，提出了贷款组合的盈余过程，得到了有限离散时间下的一个破产模型；并且利用该破产模型推导出单一贷款额结构和多个贷款额结构下的破产概率及其递归公式。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。